Answer :
To determine the domain of the function [tex]\(h(x) = \sqrt{x - 7} + 5\)[/tex], we need to focus on the part of the function that involves a square root.
1. Understand the restriction on square roots:
The expression inside the square root must be non-negative because you cannot take the square root of a negative number in the set of real numbers.
2. Set up the inequality:
For [tex]\( \sqrt{x - 7} \)[/tex] to be defined, the expression [tex]\( x - 7 \)[/tex] must be greater than or equal to zero. So, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
3. Solve the inequality:
To solve [tex]\( x - 7 \geq 0 \)[/tex], we simply add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
4. Determine the domain:
The solution to the inequality tells us that for the function [tex]\( h(x) \)[/tex] to be defined, [tex]\( x \)[/tex] must be greater than or equal to 7. Therefore, the domain of the function is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
1. Understand the restriction on square roots:
The expression inside the square root must be non-negative because you cannot take the square root of a negative number in the set of real numbers.
2. Set up the inequality:
For [tex]\( \sqrt{x - 7} \)[/tex] to be defined, the expression [tex]\( x - 7 \)[/tex] must be greater than or equal to zero. So, we set up the inequality:
[tex]\[ x - 7 \geq 0 \][/tex]
3. Solve the inequality:
To solve [tex]\( x - 7 \geq 0 \)[/tex], we simply add 7 to both sides:
[tex]\[ x \geq 7 \][/tex]
4. Determine the domain:
The solution to the inequality tells us that for the function [tex]\( h(x) \)[/tex] to be defined, [tex]\( x \)[/tex] must be greater than or equal to 7. Therefore, the domain of the function is all real numbers [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex].
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
